WASHINGTON — President Barack Obama‘s healthcare law, despite a rocky rollout and determined opposition from critics, already has spurred the largest expansion in health coverage in America in half a century, national surveys and enrollment data show.

As the law’s initial enrollment period closes, at least 9.5 million previously uninsured people have gained coverage. Some have done so through marketplaces created by the law, some through other private insurance and others through Medicaid, which has expanded under the law in about half the states. The tally draws from a review of state and federal enrollment reports, surveys and interviews with insurance executives and government officials nationwide.

The Affordable Care Act still faces major challenges, particularly the risk of premium hikes next year that could drive away newly insured customers. But the increased coverage so far amounts to substantial progress toward one of the law’s principal goals and is the most significant expansion since the creation of Medicare and Medicaid in 1965.

The millions of newly insured also create a politically important constituency that may complicate any future Republican repeal efforts. Precise figures on national health coverage will not be available for months. But available data indicate:

• At least 6 million people have signed up for health coverage on the new marketplaces, about one-third of whom were previously uninsured.

• A February survey by consulting firm McKinsey & Co. found 27% of new enrollees were previously uninsured, but newer survey data from the nonprofit Rand Corp. and reports from marketplace officials in several states suggest that share increased in March.

• At least 4.5 million previously uninsured adults have signed up for state Medicaid programs, according to Rand’s unpublished survey data, which were shared with The Times. That tracks with estimates from Avalere Health, a consulting firm that is closely following the law’s implementation.

• An additional 3 million young adults have gained coverage in recent years through a provision of the law that enables dependent children to remain on their parents’ health plans until they turn 26, according to national health insurance surveys from the federal Centers for Disease Control and Prevention.

• About 9 million people have bought health plans directly from insurers, instead of using the marketplaces, Rand found. The vast majority of these people were previously insured.

• Fewer than a million people who had health plans in 2013 are now uninsured because their plans were canceled for not meeting new standards set by the law, the Rand survey indicates.

Republican critics of the law have suggested that the cancellations last fall have led to a net reduction in coverage.

That is not supported by survey data or insurance companies, many of which report they have retained the vast majority of their 2013 customers by renewing old policies, which is permitted in about half the states, or by moving customers to new plans.

“We are talking about a very small fraction of the country” who lost coverage, said Katherine Carman, a Rand economist who is overseeing the survey.

Rand has been polling 3,300 Americans monthly about their insurance choices since last fall. Researchers found that the share of adults ages 18 to 64 without health insurance has declined from 20.9% last fall to 16.6% as of March 22.

The decrease parallels a similar drop recorded by Gallup, which found in its national polling that the uninsured rate among adults had declined from 18% in the final quarter of last year to 15.9% through the first two months of 2014. Gallup’s overall uninsured rate is lower than Rand’s because it includes seniors on Medicare.

Gallup Editor in Chief Frank Newport said that March polling, which has not been released yet, indicates the uninsured rate has declined further.

“While it is important to be cautious, the logical conclusion is that the law is having an effect,” he said.

Although estimates vary, about 45 million to 48 million people are believed to have been uninsured before the marketplaces opened last year.

The survey data are bolstered by the experiences of insurance companies and state governments, which are tracking enrollment in public and private coverage.

“We are on target to exceed what was estimated,” Lisa Sbrana, counsel for New York’s insurance marketplace, said on a recent call organized by Families USA, a Washington-based advocacy group that supports the law. About 70% of New Yorkers signing up for coverage through the marketplace or Medicaid were previously uninsured, Sbrana said.

In Kentucky, about 75% of the state residents signing up on that state’s marketplace or for Medicaid had no insurance, a state study indicates. As of Friday, more than 280,000 new people had enrolled in Medicaid in Kentucky, or nearly 91% of the residents officials estimated would become eligible for the program this year.

Florida Blue, that state’s dominant insurer, also now expects to gain customers after sign-ups were initially slowed by problems with the federal HealthCare.gov site last fall.

Around Philadelphia, Independence Blue Cross has more than doubled its customers since last year. The company’s New Jersey subsidiary, AmeriHealth New Jersey, has seen a nearly sevenfold increase.

Some insurers are finding that most of the new customers are coming through direct sales to individuals, not the law’s new marketplaces. Blue Cross Blue Shield of Minnesota, for example, says more than 90% of its sales have not been on the state marketplace. Wellmark Blue Cross and Blue Shield, the dominant insurer in Iowa and South Dakota, is seeing growth, even though it elected to stay off the marketplaces this year.

Regardless of whether consumers buy through the marketplaces or directly from insurance companies, they form part of the same risk pool, so both groups are crucial to the law’s sustainability.

Long-term stability could be undermined if newly insured people do not pay their bills or if they drop coverage in coming months because they are unhappy about the high deductibles or narrow doctor and hospital networks some plans offer.

Some people have had to pay higher premiums to replace old plans that did not comply with the law’s consumer standards.

More ominously, some insurance industry officials are warning they may raise rates substantially next year. Major rate hikes could push out healthy consumers, undermining the law’s marketplaces and recharging political opposition.

“The real question is, have they built a system that is sustainable?” said Caroline Pearson, senior vice president at Avalere Health. “Premiums will be the single most important thing that will determine that.”

But the solid enrollment in the first year has built a foundation that for now appears robust enough to support more growth next year.

In several states, including Rhode Island, Connecticut, Kentucky, Iowa and South Dakota, more insurers are looking to join state marketplaces when second-year enrollment begins this fall, according to marketplace and insurance industry officials.

And after initial resistance, a growing number of states with GOP governors or legislatures are looking to expand coverage further.

New Hampshire’s Legislature just voted to expand its Medicaid program. Utah, Indiana and Pennsylvania are looking for ways to do the same.